a) `sin(x-\frac{π}{2})=sin\frac{2π}{3}`
⇔ $\left [\begin{array}{l} x-\dfrac{π}{2}=\dfrac{2π}{3}+k2π \\ x-\dfrac{π}{2}=π-\dfrac{2π}{3}+k2π \end{array} \right.$
⇔ $\left [\begin{array}{l} x=\dfrac{7π}{6}+k2π \\ x=\dfrac{5π}{6}+k2π \end{array} \right. \ (k∈\mathbb{Z})$
b) `sin(x-30^o)=sin20^o`
⇔ $\left [\begin{array}{l} x-30^o=20^o+k360^o \\ x-30^o=180^o-20^o+k360^o \end{array} \right.$
⇔ $\left [\begin{array}{l} x=50^o+k360^o \\ x=190^o+k360^o \end{array} \right. \ (k∈\mathbb{Z})$
c) `2sinx=-1`
⇔ `sinx=-\frac{1}{2}`
⇔ `sinx=sin-\frac{π}{6}`
⇔ $\left [\begin{array}{l} x=-\dfrac{\pi}{6}+k2π \\ x=\dfrac{7π}{6}+k2π \end{array} \right. \ (k∈\mathbb{Z})$
